Aceituna Paradise is a popular restaurant in Montana that focuses on Mediterranean cuisine, offering a rich menu that highlights the healthy ingredients characteristic of Spain, Italy and Greece combined. The restaurant is particularly known for its dishes that incorporate cold pressed extra virgin olive oil $($Evoo$).$ This brings a distinctive taste to salads, pastas, and grilled meats and vegetables dishes.

Aceituna Paradise follows a periodic review policy for this product. Julia Flores, Head Chef, reviews the stock and places an order of Evoo every $4$ weeks, as this makes it more convenient for the supplier. In compensation for this, the supplier will occasionally send surprise batches of Evoo from exclusive olive varieties from the Mediterranean coast, allowing Aceituna Paradise to offer seasonal menus with rare and unique flavors to customers.

The cost of Evoo is $$100$ per case, which includes several bottles. The lead time for receiving an order is $2$ weeks, and Aceituna Paradise does not take ownership of the product until it arrives at the restaurant. The demand of Evoo at the restaurant is normally distributed with a mean of $7816$ cases per year and a standard deviation of $1763$ cases per year. There is an annual holding rate of $10\%.$

Finally, Aceituna Paradise has set a k$=1\mathrm{.}25$ for the inventory policy.

Using the inventory policy mentioned, answer the following questions. Assume $50$ weeks per year for all calculations.

What is the order$-$up$-$to$-$point $($S$)?$